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ULTRAFAST DYNAMICAL RESPONSE OF THE PROTOTYPE MOTT COMPOUND V2O3
B. Mansart1,
D. Boschetto2 and M. Marsi1
1Laboratoire de Physique des Solides, UMR 8502, Université Paris-Sud, 91405 Orsay, France
2 Laboratoire d’Optique Appliquée, ENSTA, CNRS, Ecole Polytechnique, 91761 Palaiseau, France
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Phase diagram and Mott transition in (V1-xCrx)2O3
Mott transition: localisation of electrons Coulomb Repulsion > Kinetic Energy.
prototype Metal-Insulator transition:
no symmetry breaking
McWhan et al., PRL 27 (1971)
Limelette et al., Science (2003)
Paramagnetic Metal (PM) -Paramagnetic Insulator (PI): resistivity changes of 7 orders of magnitude
V
O o
PMPI
AFI Kuroda et al. , PRB 16 (1977)
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Time-resolved reflectivity on V2O3
wavelength: 800 nmpulse duration: 45 fsrepetition rate 1 kHzPump and probe polarizations orthogonal
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Time-resolved reflectivity on V2O3
wavelength: 800 nmpulse duration: 45 fsrepetition rate 1 kHz
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Time-resolved reflectivity on V2O3
1. Ultrafast peak: electronic excitation
wavelength: 800 nmpulse duration: 45 fsrepetition rate 1 kHz
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Time-resolved reflectivity on V2O3
1. Ultrafast peak: electronic excitation
wavelength: 800 nmpulse duration: 45 fsrepetition rate 1 kHz
2. Coherent Optical A1g Phonon
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Time-resolved reflectivity on V2O3
1. Ultrafast peak: electronic excitation
wavelength: 800 nmpulse duration: 45 fsrepetition rate 1 kHz
2. Coherent Optical A1g Phonon
3. Coherent Acoustic wave propagation
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Ultrafast electronic excitation
Electronic peak represents the ultrafast excitation and relaxation of electrons.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Ultrafast electronic excitation
Electronic peak represents the ultrafast excitation and relaxation of electrons.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Ultrafast electronic excitation
Electronic peak represents the ultrafast excitation and relaxation of electrons.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Ultrafast electronic excitation
Electronic peak represents the ultrafast excitation and relaxation of electrons.
Electronic Peak: Intensity linear with pump fluence, width increasing with pump fluence.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
In V2O3 compounds, the thermalization time depends on pump fluence. It is ~130 fs: faster than normal metals and others strongly correlated materials.
Ultrafast electronic excitation analysis
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Relaxation of hot electrons: Two Temperatures Model (TTM).
Ultrafast electronic excitation analysis
LEL
L TTgt
TC
LEE
Es
EE TTg
z
T
ztI
l
A
t
TC
)(2
In V2O3 compounds, the thermalization time depends on pump fluence. It is ~130 fs: faster than normal metals and others strongly correlated materials.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Ultrafast electronic excitation analysis
LEL
L TTgt
TC
LEE
Es
EE TTg
z
T
ztI
l
A
t
TC
)(2
In V2O3 compounds, the thermalization time depends on pump fluence. It is ~130 fs: faster than normal metals and others strongly correlated materials.
Relaxation of hot electrons: Two Temperatures Model (TTM).
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Ultrafast electronic excitation analysis
LEL
L TTgt
TC
LEE
Es
EE TTg
z
T
ztI
l
A
t
TC
)(2
With this model, one obtains a very high g value, 1000 times larger than gold.
Possibly we underestimate the electron diffusion term E, which could be higher in the photoexcited state than at equilibrium .
In V2O3 compounds, the thermalisation time depends on pump fluence. It is ~130 fs: faster than normal metals and others strongly correlated materials.
Relaxation of hot electrons: Two Temperatures Model (TTM).
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
V
V
Optical phonon: pump fluence study
A1g
mode
Phonon frequency: 8.12 THz at 200K
Phonon lifetime: 630 fs at 200K
frequency blue-shifted with respect to Raman measurements (6.23THz, Kuroda et al., PRB 16 (1977)). Consistent with previous measurements on undoped V2O3.(Misochko et al., PRB 58, (1998)).
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
V
V
Optical phonon: pump fluence study
A1g
mode
The frequency and lifetime of this mode don’t depend on the thermodynamic phase (metal vs insulator).
Phonon frequency: 8.12 THz at 200K
Phonon lifetime: 630 fs at 200K
frequency blue-shifted with respect to Raman measurements (6.23THz, Kuroda et al., PRB 16 (1977)). Consistent with previous measurements on undoped V2O3.(Misochko et al., PRB 58, (1998)).
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Coherent Acoustic Wave: sample orientation effect
hexagonal c-axis
V
O o Experimental geometry and c-axis orientation
Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe cos i
We only detect the acoustic wave propagating along the incident plane symmetry axis.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Coherent Acoustic Wave: sample orientation effect
hexagonal c-axis
V
O o Experimental geometry and c-axis orientation
Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe cos i
We only detect the acoustic wave propagating along the incident plane symmetry axis.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Coherent Acoustic Wave: sample orientation effect
hexagonal c-axis
V
O o Experimental geometry and c-axis orientation
Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe cos i
We only detect the acoustic wave propagating along the incident plane symmetry axis.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Coherent Acoustic Wave: sample orientation effect
hexagonal c-axis
V
O o Experimental geometry and c-axis orientation
Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe cos i
We only detect the acoustic wave propagating along the incident plane symmetry axis.
Along the c-axis, the detected acoustic wave is strongly reduced.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Acoustic wave: Thermodynamic phase effects
Insulating phase (PI) Metallic phase (PM)
PM
PI
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Acoustic wave: Thermodynamic phase effects
Insulating phase (PI) Metallic phase (PM)
PM
PI
Coherent acoustic oscillation intensity linear in pump fluence, identical in metal and insulator.
The lifetime is longer in the Insulating phase.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Acoustic wave: Thermodynamic phase effects
Insulating phase (PI) Metallic phase (PM)
PM
PI
Strong effects of the thermodynamic phase (metal vs insulator) on the mean value (baseline) of the coherent oscillation.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Conclusions and perspectives
We measured the ultrafast response of the prototype Mott compound V2O3.
The coherent oscillations don’t depend on the thermodynamic phase.
Coherent acoustic oscillations show a strong dependence on crystal orientation with respect to the laser propagation direction.
Difference between metal and insulator: mean value of the reflectivity on the picosecond time-scale. Potentially important also for other materials presenting metal-insulator transitions.
Perspectives: explore the dependence on the pump and probe
wavelengths.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
References
Pump-probe reflectivity measurements :
R.Merlin, Solid State Commun. 102, 207 (1997) Y-X.Yan and K.A.Nelson, J.Chem.Phys. 87, 6257 (1987) D.Boschetto et al., Phys.Rev.Lett. 100, 027404 (2008) C.Thomsen et al., Phys.Rev.B 34, 4129 (1986) L. Brillouin, Ann. de Phys. (Paris) 17, 88 (1922)
Phonons in V2O3:
N.Kuroda and H.Y.Fan, Phys.Rev.B 16, 5003 (1977) O.V.Misochko et al., Phys.Rev.B 58, 12789 (1998) Md.Motin Seikh et al., Solid State Commun. 138, 466 (2006) S.R.Hassan, A.Georges et al., Phys.Rev.Lett. 94, 036402
(2005)
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Synchronous detection:lock-in amplifier
LaserLaser
ReferenceReference
pumppump
probeprobe
delay linedelay linechopper
Sample
PD1PD1
PP
L1L1
L2L2
/2/20.1 90
Amplitude Phase
Experimental Setup
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
N.Kuroda and H.Y.Fan, Phys.Rev.B 16, 5003 (1977)
Raman spectrum of V2O3
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Reflectivity of V2O3
L. Baldassarre et al., PRB 77, 113107 (2008)
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Difference Metal-Insulator: coherent acoustic wave
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Difference Metal-Insulator: coherent acoustic wave
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
DMFT calculations for Mott compounds
Georges et al. RMP (1996)
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Photoemission experiments on (V1-xCrx)2O3 x=0.011
-2.0 -1.5 -1.0 -0.5 0.0binding energy (eV)
métal 200K isolant 300K Ag
(V1-xCrx)2O3 x=0.011
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Spectromicroscopy experiments on (V1-xCrx)2O3 x=0.011
Phase separation observed in photoemission experiments.
In agrement with the disapearrance of the coherent acoustic wave in the metallic phase of the same sample.
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Pump pulse
Excitation of electrons close to Fermi level
Variation of electronic density
Excitation of coherent phonons
Variation of electron-phonon collision rate
Variation of the dieletric function
Variation of the
reflectivity
Excitation and detection of coherents optical phonons
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Principle of the pump-probe reflectivity: measure of the probe reflectivity as a function of time delay between pump and probe.
Theoretical considerations on pump-probe reflectivity
t
Sample
detector
pump
probe
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Out of equilibrium, optical properties of solids depends on several parameters: electron density, electronic effective mass and electron-phonon collision rate.
In metals, a good approximation is the Drude model, giving the
dielectric function in terms of these three parameters:
p being the plasma frequency:
and e-ph is the electron-phonon collision frequency:
Where ve is electron velocity, nph is phonon density and q is the atomic displacement.
ephphe vtqtn )( )( 2
irphe
phe
p
phe
p ii
1
22
2
22
2
*
22 )(4
e
ep m
tne
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
The reflectivity is always given by Fresnel equations:
After electron excitation by the pump pulse, electron density and electron-phonon collision rate change, and so the dielectric function changes as well.
This causes variations in reflectivity, as the following equation:
If we know the expression of dielectric function, we can get the derivatives with respect to ne and e-ph, and so obtain an analytic expression for the transient reflectivity.
2
2/1
2/1
11
R
phephe
i
iphe
r
re
e
i
ie
r
r
RRn
n
R
n
RR
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
The electron density is proportional to electronic temperature:
The excited phonon density is proportional to the lattice temperature, Debye temperature and atomic density as:
So for the electron-phonon collision rate:
max
)( )(e
e
e
e
TtT
ntn
a
D
lph n
TtTtn )()(
000
)(2)()(q
tqT
tTt l
phe
phe
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Finally, the electronic and lattice temperatures can be given by the Two-Temperature Model equations:
Where Ce and Cl are respectively heat capacity of electrons and lattice, A is absorption coefficient, ls the penetration depth, e the heat diffusivity of electrons and g the electron-phonon coupling constant.
And changes in reflectivity can be written in the form:
lee
es
ee TTg
z
T
ztI
l
A
t
TC
)(2
lel
l TTgt
TC
tAtTAtTAR phllee cos )( )( 220
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Phenomenologic model of Thomsen
Excitation and detection of coherent acoustic phonons
Pump pulse arriving along z-axis
Deposition of energy in the skin depth
Temperature gradient: z-dependent thermic constraint
Creation of a deformation wave along z-axis (longitudinal acoustic phonon))
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Detection of acoustic waves:
Diffraction of the probe beam on acoustic waves propagating in the material (the probe acts as a filter by selecting the measured wave)
qphonon = 2 n ksonde cos i
Sound velocity: = vs q
Final expression for the transient reflectivity:t
sonde
isac etnvAtR
cos4cos)(
Sample
detector
probe
i
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Relaxation Times
Manganites: spin-lattice relaxation:between 25 ps and 300 ps (as a function of temperature) Averitt and Taylor, J. Phys:Condens. Matter 14, R1357 (2002)
Blue Bronze: quasiparticle decay time 530 fs, Sagara, PHd thesis
Ultrafast Dynamic Imaging of Matter II, Ischia 2009
Ccl: effet phase thermo Electron-phonon coupling fundamental in Mott transition and in general in strongly
correlated systems Electronic excitation peak e-ph coupling from ultrafast response Optical phonon and acoustic phonon have to be understood in order to completely
describe the ultrafast response and the correct lineshape of the electronic excitation Show how one can extract e-ph coupling from electronic excitation (one exemple) optical phonon: (no) polarization dependence Acoustic phonon: (strong) polarization dependence (?) Optical phonon: (very weak) phase dependence (normal for Mott material) Acoustic phonon: thermodynamic phase dependence
Conclusions: 1) we measured e-ph coupling for prototype Mott compound V2O3 2) in order to correctly measure it, understand overall ultrafast response 3) overall ultrafast response depends on LATTICE oscillations (polarization AND phase
dependence) even for purely ELECTRONIC Mott system 4) these effects may in general contribute to the ultrafast response of all strongly
correlated materials (even those where electronic transitions are associated to structural symmetry changes)